-12x^2+12=156x

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Solution for -12x^2+12=156x equation:


Simplifying
-12x2 + 12 = 156x

Reorder the terms:
12 + -12x2 = 156x

Solving
12 + -12x2 = 156x

Solving for variable 'x'.

Reorder the terms:
12 + -156x + -12x2 = 156x + -156x

Combine like terms: 156x + -156x = 0
12 + -156x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + -13x + -1x2) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(1 + -13x + -1x2)' equal to zero and attempt to solve: Simplifying 1 + -13x + -1x2 = 0 Solving 1 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 13x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 13x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 13x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 13x + x2 = 0 + 1 13x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 13x + x2 = 1 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 1 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 1 + 42.25 Combine like terms: 1 + 42.25 = 43.25 42.25 + 13x + x2 = 43.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + 6.5) equal to 6.576473219 and -6.576473219.

Subproblem 1

x + 6.5 = 6.576473219 Simplifying x + 6.5 = 6.576473219 Reorder the terms: 6.5 + x = 6.576473219 Solving 6.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.576473219 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.576473219 + -6.5 x = 6.576473219 + -6.5 Combine like terms: 6.576473219 + -6.5 = 0.076473219 x = 0.076473219 Simplifying x = 0.076473219

Subproblem 2

x + 6.5 = -6.576473219 Simplifying x + 6.5 = -6.576473219 Reorder the terms: 6.5 + x = -6.576473219 Solving 6.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.576473219 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.576473219 + -6.5 x = -6.576473219 + -6.5 Combine like terms: -6.576473219 + -6.5 = -13.076473219 x = -13.076473219 Simplifying x = -13.076473219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.076473219, -13.076473219}

Solution

x = {0.076473219, -13.076473219}

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